A note on p-injectivity

• Autorzy: Yue Chi Ming R.
• Języki publikacji: EN

Abstrakty

EN

This note contains results related to p-injectivity and YJ-injectivity. Conditions are given for rings to be (i) V-rings; (ii) VNR; (iii) self-injective regular or strongly regular. A characterization of principal ideal quasi-Frobenius rings is given in terms of p-injectivity. A condition is given for a fully right idempotent ring to have a von Neumann regular classical left quotient ring. It is also proved that if A is a fully right idempotent, right Goldie ring, then every two-sided ideal of A is generated by a central idempotent.

Słowa kluczowe

EN

Von Neumann regular; v-rings; flatness; p-injectivity; Jacobson radical; quasi-Frobeniusean

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 1
• Strony: 45--54
• Opis fizyczny: Bibliogr. 35 poz.

Twórcy

autor

Yue Chi Ming R.

• Universite Paris VII-Denis Diderot, UFR de Maths.-UMR 9994 CNRS, 2, Place Jussieu, 75251 Paris Cedex 05, France

Bibliografia

• [1] G. Baccella, Generalized V-rings and von Neumann regular rings. Rend Sem. Mat. Univ. Padova 72 (1984), 117-133.
• [2] J .L. Chen, On von Neumann regular rings and SF-rings. Math. Japonica 36 (1991), 1123-1127.
• [3] J.L. Chen, N.Q. Ding, On general principally injective rings. Comm. Algebra 27 (1999), 2097-2116.
• [4] N.Q. Ding, J.L. Chen, Rings whose simple singular modules are YJ-injective. Math. Japonica (1994), 191-195.
• [5] C. Faith, Algebra II: Ring Theory, Springer-Verlag, 1976.
• [6] C. Faith, Rings and things and a fine array of twentieth century associative algebra. AMS Math. Surveys and Monographs 65 (1999).
• [7] K.R. Goodearl, Ring Theory: Non-Singular Rings and Modules. Marcel Dekker, New York, 1976.
• [8] K.R. Goodearl, Von Neumann Regular Rings. Pitman, London, 1979.
• [9] Y. Hirano, On non-singular p-injective rings. Publ. Math. 38 (1994), 455-461.
• [10] Y. Hirano, H. Tominaga, Regular rings, V-rings and their generalizations. Hiroshima Math. J. 9 (1979), 137-149 .
• [11] D.V. Huynh, N.V. Dung, P.F. Smith and R. Wisbauer, Extending Modules. Pitman, London (1994).
• [12] N.K. Kim, S.B. Nam and J.Y. Kim, On simple singular GP-injective modules. Comm. Algebra 27 (1999), 2087-2096.
• [13] T.Y . Lam, Lectures on Modules and Rings. Graduate texts in Math. Springer 189 (1998).
• [14] S.H. Mohamed, B.J. Muëller, Continuous and discrete modules. LMS Lecture notes 47 (C.U .P.) (1990).
• [15] W.K. Nicholson, M.F. Yousif, Principally injective rings. J. Algebra 174 (1995), 77-93.
• [16] G. Puninski, R. Wisbauer and M. Yousif, On p-injective rings. Glasgow Math. J. 37 (1995), 373-378.
• [17] A. Shamsuddin, Homological properties of SF-rings. Bull. Australian Math. Soc. 55 (1997), 327-333.
• [18] A.A. Tuganbaev, Rings whose non-zero modules have maximal submodules. J. Math. Sci. 119 (2002), 1589-1640.
• [19] R. Wisbauer, Foundations of Module and Ring Theory. Gordon and Breach New York, 1991.
• [20] W. Xue, A note on YJ-injectivity. Riv. Mat . Univ. Parma (6)1 (1998), 31-37.
• [21] R. Yue Chi Ming, On von Neumann regular rings. Proc. Edinburgh Math. Soc. 19 (1974), 89-91.
• [22] R. Yue Chi Ming, On simple p-injective modules. Math. Japonica 19 (1974), 173-176.
• [23] R. Yue Chi Ming, On von Neumann regular rings, VI. Rend. Sem. Mat. Univ. Torino 39 (1981), 75-84.
• [24] R. Yue Chi Ming, On regular rings and self injective rings, II. Glasnik Mat . 18(38) (1983), 221-229.
• [25] R. Yue Chi Ming, On von Neumann regular rings, X. Collect Math. 34 (1983), 81-94.
• [26] R. Yue Chi Ming, Remarks on strongly regular rings. Portugal Math. 44 (1987), 101-112.
• [27] R. Yue Chi Ming, On injectivity and p-injectivity. J. Math. Kyoto Univ. 27 (1987), 439-452.
• [28] R. Yue Chi Ming, On von Neumann regular rings, XV. Acta Math. Vietnam 13 (1988), 71-79.
• [29] R. Yue Chi Ming, On self-injective rings and quasi-Frobeniusean rings. Rend. Mat. Univ. Trieste 20 (1988), 265-274.
• [30] R. Yue Chi Ming, On von Neumann regularity, injectivity and flatness. Yokohama Math. J. 43 (1995), 37-44.
• [31] R. Yue Chi Ming, On injectivity and p-injectivity, II. Soochow J. Math. 21(1995), 401-412.
• [32] R. Yue Chi Ming, On MI-rings and regular rings. Rev. Roumaine Math. Pures Appl. 45 (2000), 521 -530.
• [33] R. Yue Chi Ming, On injectivity and p-injectivity, III. Riv. Mat. Univ. Parma (6)4 (2001), 45-50.
• [34] J.L. Zhang, Fully idempotent rings whose every maximal left ideal is an ideal. Chinese Sci. Bull. 37 (1992), 1065-1068.
• [35] J.L. Zhang, J. Wu, Generalized of principal injectivity. Algebra Colloquium 6 (1999), 277-282.